Manuscript Oai365-A@1 · Oai365-A.tex · lemma · a3840e3d

Lemma: Polarization

The same-patch elliptic boundary object › Variational definition · lines 729–744 · proof included or linked

Oai365-A@1#lem:polarization

The energy determines the whole complex form:

B (f, h) = \frac{1}{4} [Q (f + h) - Q (f - h) - i Q (f + ih) + i Q (f - ih)] .

Proof. Expand each quadratic expression using sesquilinearity. The first difference is $4 Re B (f, h)$ . The second, with the displayed signs, contributes $4 i Im B (f, h)$ .

Displayed formulas in this passage

unlabeled · line 732
$B (f, h) = \frac{1}{4} [Q (f + h) - Q (f - h) - i Q (f + ih) + i Q (f - ih)] .$

Nearby in this section

section: Variational definition
lemma: Lemma: Well-posedness and continuity
section: Variational definition